Relativity
makes the following claim:
“Events which
are simultaneous with reference to the embankment are not simultaneous with
respect to the train, and vice versa (relativity of simultaneity). Every
reference-body (coordinate system) has its own particular time; unless we are
told the reference-body to which the statement of time refers, there is no
meaning in a statement of the time of an event.
“Now before the
advent of the theory of relativity, it had always tacitly been assumed in
physics that the statement of time had an absolute significance, i.e., that it
is independent of the state of motion of a body of reference. But we have just
seen that this assumption is incompatible with the most natural definition of
simultaneity.” (Relativity Chapter
Nine)
Einstein comes
to this conclusion by using the thought experiment of two bolts of lightning
striking either end of the train. An observer along the embankment sees the
lightning strikes as simultaneous, while an observer inside the train, moving
with respect to the embankment, is also moving toward the lightning flash at
the front of the train, and receding from the flash at the rear of the train.
The train’s observer will thus see the flash at the front of the train first,
and conclude that the lightning struck the front of the train first.
Einstein uses
this simple thought experiment to draw sweeping conclusions about the nature of
time and simultaneity.
But adding a
tiny detail to Einstein’s thought experiment will actually invalidate his
conclusions about the relativity of simultaneity.
Let’s take
Einstein’s thought experiment and add a simple device I will call a
“simultaneity detector,” or SD. This device consists of several parts. First is
a clock at the center of the train carriage. This clock need not be
synchronized with clocks at the front and back of the train, or anywhere else.
It’s simply a clock whose time can be independent of any other clock, since it will only be recording its reading of an event in its immediate vicinity. Next,
there is a lightning rod at each end of the train, equidistant from the central
clock. Each rod has an attached length of wire that feeds into the central
clock. Each wire is exactly the same length as the other. The central clock is able to
detect when a current reaches it through either wire, and records the time at
that instant, so that any observer will be able to consult the clock for a
readout of the exact time (according to that clock) that a current was detected in either wire.
Now, when the
lightning bolts strike the lightning rods at either end of the train, a current
will flow through the rod’s respective wire and reach the central clock, where the time
of the current’s detection will be recorded.
How does this
alter Einstein’s experiment in any significant way? Well, it takes the
determination of simultaneity out of the realm of relativity and puts it into
classical Newtonian-Galilean physics. This is because the current in the wire
will not behave as the lightning flashes of Einstein's experiment does. Consider: electrical current is a flow of
electrons within a wire. The wire is moving along with the train, and hence
will obey classic addition of velocities, which light does not. Thus, the
detection of current in the wires will be an arbiter of simultaneity.
How so?
Well, if the
embankment observer sees the lightning strikes as simultaneous, while he will
see the train’s observer rushing toward the forward flash and receding from the
rear-ward flash, he will not likewise see the train’s observer rushing toward
the front current and away from the rear current. The two currents will reach
the central clock together and will each receive the same time stamp from the
clock.
However, the
train’s observer will see things differently. He will see the flashes as
non-simultaneous, yet will be astonished to find that the central clock tells
him the currents have the same time stamp. He will thus conclude that he must
be moving.
Unlike with
Einstein’s thought experiment, where the observers are free to accept that they
disagree on simultaneity because there are no actual, physical consequences of
such disagreement, the central clock cannot physically display different time
stamps depending upon who consults it. There is an absolute fact as to what
time the currents were detected, according to the central clock.
You might
wonder why I don’t just have the central clock recording the time at which each
flash reaches it. I’ll reiterate my earlier reasoning for you: the current in
the wire obeys classic addition of velocities, while the light flashes,
according to relativity, do not. The current in the wire is not light; it is
movement of electrons.
Think about it.
If the observer on the embankment were to consider the current in the way that
he considers light, then he must also consider the train observer in the same
way. Light does not hold to addition of velocities. If the electrons and the
train observer likewise did not hold to such, then if the train’s observer were
to walk from the rear of the train toward the front, then the rear wall would
be racing toward him even as the front wall was receding, just as with the
flashes of light. Same with the current. Even as the current from the rear
flowed through the wire, the central clock would be receding from it even as
the central clock raced toward the front current, and the central clock would
stamp the current from the front as reaching it first, in conflict with the
embankment observer’s assertion that the strikes were simultaneous.
You might
object that the train’s observer would indeed drift backward if he were to jump
up and down; he only moves forward with the train because he is attached to it.
But this violates physics; remember Newton ’s
first law of motion, and Galilean relativity? Relativity doesn’t discard those.
If you believe that the Earth is rotating, then if these laws weren’t true, you
could jump straight up in the air and land in a different spot.
You might
further object that I am incorrect. Current in a wire behaves the same as
light, and thus the time stamps from the central clock will confirm the train
observer’s conclusion that the front strike happened first. OK. But in such a
case, we are left with physical evidence that contradicts the embankment
observer’s assessment that the strikes were simultaneous. We now have the
testimony of the train observer and the testimony of the central clock to
contradict the embankment observer. This would allow the train’s observer to
assert that the embankment observer is the one in motion, which on the face of
it seems okay, since we now have reciprocity, one of the hallmarks of special
relativity. Each observer is allowed to conclude that he is at rest while the
other observer is the one in motion. But this objection, as I’ve pointed out
above, comes at the cost of violating physical laws which relativity retains:
“…in reality there is not the least incompatibility between the principle of
relativity, and that by systematically holding fast to both these laws a
logically rigid theory could be arrived at.” (Relativity Chapter Seven).
As simple
evidence that electrons must hold to classical relativity, I offer the
following: our bodies contain many, many electrons. So if you try to assert
that electrons don’t hold to classical relativity and instead behave as light
does, then you must throw out the classical principle of relativity, since
EVERYTHING within the rocket (rocket, train, whatever) is made of electrons.
Even the walls of the train. So if the ship, train, rocket, whatever, is moving
at near light speed, in what sense could the outside observer say that he sees
the train observer racing toward the forward flash even as he recedes from the
rear flash? Matter does not behave like light. Matter adheres to addition of
velocities, light does not.
NOTE TO SELF:
But perhaps matter behaves more like light the faster it goes, so that at near
light speed it is a lot more like light than matter. And perhaps in such a case
the central clock actually CAN display two different time stamps depending upon
who observes it, existing in both states until one or the other observes it,
much like Schrödinger’s Cat. Connection between relativity and quantum
mechanics? Even such a situation would still be a blow to relativity, since, as
evidenced by Einstein’s thought experiments, relativity still considers matter
to behave like matter even at relativistic speeds, as evidenced by matter
adhering to the addition of velocities in the thought experiments
Now, I should
point out that the weakness of the preceding is my assertion that electricity
flowing through a wire does not behave like light, instead obeying addition of
velocities. I can find nothing to support this assertion. I recall stumbling
across an article long ago that confirmed this, but I have no idea where I
stumbled across that article, and I can find nothing to support me now. But I
can find nothing to refute my assertion either. But it seems reasonable to me
that since electrons carry the flow of electrical energy through a wire, then
they can’t behave in such a way that, were someone in a moving spaceship to
flick a light switch on the front wall, then a light bulb at the center of the
ship would turn on sooner than it would if the person flicked a switch on the
rear wall. Such behavior would require the electrons to forsake the addition of
velocities, and if electrons in a wire do so, why shouldn’t my entire body also
forsake the addition of velocities? Such behavior would lead to a different
world than the one we observe.
Anyway,
realizing as I do that the weakness of my preceding thought experiment is its
reliance on the wire current not behaving like light, I have a few variations
on the thought experiment, using things that definitely don’t have a relation
to electricity. These are earlier iterations of the above thought experiment. I
actually wrote the following well before I came up with the final version as
above.
Imagine a
cube-shaped ship moving through space. There is relativistic motion between
this ship and an outside observer. All the dimensions of the ship are exactly
equal as measured by an observer within the ship. Also, there is a strip of
some sort of substance connecting the forward wall with the aft wall, like a
string or something. The strip, when struck by lightning, undergoes a chemical
reaction that proceeds along the string from the source of the strike, so that
it changes to a different color, the different color depending upon the source
of the strike. Say a strike on the forward wall causes the string to turn blue
traveling backward, and a strike on the aft wall causes the string to turn red
traveling forward. The chemical reaction stops when each reaction meets the
other.
It seems to me
that the chemical reaction will travel along the string at a constant rate that
can’t possibly depend upon the motion (or lack of it) of either the ship or an
outside observer. In other words, you can’t run into a situation where the
walls are moving toward or receding from the “leading edge” of the chemical
reaction, since the reaction is relative to the string alone rather than
relative to an observer, i.e. it’s not the same situation as light traveling
fore or aft.
Now lightning
strikes the fore and aft walls, kicking off the reaction, which travels along
the string in each direction, heading aft along the strip from the forward
wall, and running forward along the strip from the aft wall.
If simultaneity
is truly relative, then when the reactions run their course, the length of the
string that is red and the length that is blue will depend upon which observer
examines the strip. If the outside observer says the lightning strikes were
simultaneous, and he considers the ship to be in motion, then the string should
be equal lengths red and blue when he examines it, the point at which blue
turns to red being at the exact center of the ship. Likewise, when the ship’s
observer, considering the strikes to have been non-simultaneous, examines the
string, he should find that more of the string is red, the point at which red
turns to blue being off center toward the rear of the ship. If simultaneity is
truly relative, then the amount of red and blue on the string should be
different depending upon who examines it, which should be physically impossible,
therefore simultaneity cannot possibly be relative.
Here’s an even
better visualization: imagine that the fore and aft walls of the ship are
connected by a steel pipe, and that the pipe is filled with gunpowder. This is
some sort of strange gunpowder that explodes at the point where the two flames
come together, bursting the pipe. So the lightning strikes set off the
gunpowder, and a flame runs forward from the rear wall and rearward from the
front wall. Where the two flames meet, the pipe explodes, marking the spot. If
relativity is correct, then the spot at which the pipe explodes will depend
upon which observer we ask.
Better yet,
let’s put a rifle at each wall, triggered by the lightning strikes. And the
interior of a ship is a perfect vacuum, so that there’s no drag on the bullets.
According to relativity, depending upon which observer we ask, the observer at
the center of the ship is struck by both bullets at the same time, or he’s
struck by the front bullet first.
All of the
above versions transfer a relativistic problem into the realm of Galilean
relativity. You could argue that the difference in the timing of the bullet
strikes, or the difference in the amounts of red and blue on the string, or the
position at which the pipe burst, as measured by either observer, would be too
infinitesimal to measure, that such a Galilean experiment would be too
“coarse,” or lack the temporal or spatial resolution to measure such
relativistic effects, and is hence worthless, but that’s just avoiding the
issue. I could argue back that in Einstein’s thought experiment, human
observers couldn’t possibly tell with their naked eyes whether or not two
lightning strikes are simultaneous because our conscious brains lack that sort
of temporal resolution, and that Einstein’s thought experiment is worthless.
The take-home
lesson from this thought experiment is that we can’t rely on our eyes and upon
mathematical calculations to determine simultaneity. Just because someone SEES events as simultaneous or non-simultaneous, he is not justified in using mere
math to support the conclusion of his eyes. There MUST be an absolute physical
fact as to whether the lightning strikes are simultaneous or non-simultaneous.
